{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# 测试线性回归模型\n",
    "\n",
    "## 直接求解--最小二乘法\n",
    "\n",
    "> 操作步骤\n",
    "1. 导入依赖 "
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "39b1aea0bdd05f32"
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "10.0"
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号\n",
    "plt.rcParams['font.size']"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-16T08:35:58.936029500Z",
     "start_time": "2024-04-16T08:35:58.689063800Z"
    }
   },
   "id": "9251eb91da58b784"
  },
  {
   "cell_type": "markdown",
   "source": [
    "2. 生成数据"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "e559a3f7d12f336c"
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "import random\n",
    "random.seed(42)\n",
    "x = 2*np.random.rand(100, 1)\n",
    "y = 4+3*x+np.random.rand(100,1)*5"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-16T08:36:09.444690100Z",
     "start_time": "2024-04-16T08:36:09.425579700Z"
    }
   },
   "id": "e2f1c8bd84e8e778"
  },
  {
   "cell_type": "markdown",
   "source": [
    "3. 根据生成的数据画图"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "65f7ee8d718ce63d"
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.scatter(x, y, color='blue',s=10)\n",
    "plt.title('线性回归数据')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-16T08:36:12.501690400Z",
     "start_time": "2024-04-16T08:36:12.395633Z"
    }
   },
   "id": "a3853e0842ed9fcb"
  },
  {
   "cell_type": "markdown",
   "source": [
    "4. 最小二乘法求解"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "499ffbf1d36c1148"
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6.51297043]\n",
      " [2.82806798]]\n"
     ]
    }
   ],
   "source": [
    "# 最小二乘法求解\n",
    "X = np.hstack((np.ones((100,1)), x))    # 增加偏置项\n",
    "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "print(theta)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T10:24:55.424813700Z",
     "start_time": "2024-04-15T10:24:55.381541Z"
    }
   },
   "id": "a20fc7fde9f894b6"
  },
  {
   "cell_type": "markdown",
   "source": [
    "5. 画拟合曲线"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "4bfd7bfbcc94cea"
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画拟合曲线\n",
    "plt.scatter(x, y, color='red')\n",
    "plt.plot(x, theta[0]+theta[1]*x, color='blue')\n",
    "plt.title('线性回归拟合曲线')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T10:24:55.473695800Z",
     "start_time": "2024-04-15T10:24:55.392765600Z"
    }
   },
   "id": "3d7df9868a373f07"
  },
  {
   "cell_type": "markdown",
   "source": [
    "代码求解-梯度计算"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "7b09674464ab2ef4"
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 导入依赖\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# 2. 通过前面定义的数据进行训练\n",
    "linear_regressor = LinearRegression()\n",
    "linear_regressor.fit(x, y)\n",
    "\n",
    "# 3. 画拟合曲线\n",
    "plt.scatter(x, y, color='red')\n",
    "plt.plot(x, linear_regressor.predict(x), color='blue')\n",
    "plt.title('线性回归拟合曲线')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T10:24:55.552412300Z",
     "start_time": "2024-04-15T10:24:55.473695800Z"
    }
   },
   "id": "ce3184dcc52d1da5"
  },
  {
   "cell_type": "markdown",
   "source": [
    "代码求解-梯度下降法-批量梯度下降法"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "11fd3a7ca8cdcf65"
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "经过训练的theta值为 [[6.51050643]\n",
      " [2.83014666]]\n"
     ]
    }
   ],
   "source": [
    "# 1. 导入依赖\n",
    "import numpy as np\n",
    "\n",
    "# 2. 定义参数\n",
    "learning_rate = 0.01\n",
    "num_iters = 5000\n",
    "theta = np.zeros((2,1)) # 定义初始theta为2*1的零向量\n",
    "num = len(x)\n",
    "theta_route_batch = []\n",
    "\n",
    "# 3. 数据初始化\n",
    "X = np.hstack((np.ones((num,1)), x))    # 增加偏置项\n",
    "\n",
    "# 3. 代码实现梯度公式\n",
    "for iteration in range(num_iters):\n",
    "    hypothesis = np.dot(X, theta)\n",
    "    # x:m*n,theta:n*1,hypothesis:m*1\n",
    "    theta = theta - 1/num * learning_rate * np.dot(X.T , (hypothesis - y))\n",
    "    theta_route_batch.append(theta)\n",
    "    \n",
    "print(\"经过训练的theta值为\",theta)\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T10:24:55.601571100Z",
     "start_time": "2024-04-15T10:24:55.557706600Z"
    }
   },
   "id": "41a42a53f0296be0"
  },
  {
   "cell_type": "markdown",
   "source": [
    "测试不同学习率对结果的影响"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "1a8e216d8d57ad9f"
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 3 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 导入依赖\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 2. 定义训练参数\n",
    "num_iters = 5000\n",
    "theta = np.zeros((2,1)) # 定义初始theta为2*1的零向量\n",
    "num = len(x)\n",
    "\n",
    "X = np.hstack((np.ones((num,1)), x))    # 增加偏置项\n",
    "\n",
    "\n",
    "# 3. 定义训练函数\n",
    "def train(learning_rate,theta, num_iters):\n",
    "    # 2.1 绘制初始节点\n",
    "    plt.scatter(x, y, color='red')\n",
    "    for i in range(num_iters):\n",
    "        hypothesis = np.dot(X, theta)\n",
    "        theta = theta - 1/num * learning_rate * np.dot(X.T , (hypothesis - y))\n",
    "        plt.plot(x, theta[0]+theta[1]*x, color='blue')\n",
    "    plt.title('learning rate = {}'.format(learning_rate))\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "\n",
    "# 4. 定义绘图范围，进行对照实验，并分别进行绘图\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.subplot(1, 3, 1)\n",
    "train(0.01, theta, num_iters)\n",
    "plt.subplot(1, 3, 2)\n",
    "train(0.1, theta, num_iters)\n",
    "plt.subplot(1, 3, 3)\n",
    "train(0.5, theta, num_iters)\n",
    "plt.show()\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T10:25:07.947784900Z",
     "start_time": "2024-04-15T10:24:55.576571500Z"
    }
   },
   "id": "f8c31b2e50cf0ef7"
  },
  {
   "cell_type": "markdown",
   "source": [
    "代码求解-梯度下降法-随机梯度下降法"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "827ef18824516591"
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 0 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 导入依赖\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "# 2. 定义参数\n",
    "n_porch = 50\n",
    "t0 = 100\n",
    "t1 = 50\n",
    "num_iters = 500\n",
    "theta = np.zeros((2,1)) # 定义初始theta为2*1的零向量\n",
    "num = len(x)\n",
    "theta_route_random = []\n",
    "\n",
    "\n",
    "# 3. 定义学习率衰减策略函数\n",
    "def learning_rate_schedule(t):\n",
    "    return t0/(t+t1)\n",
    "\n",
    "plt.clf()\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x, y, color='red')\n",
    "plt.title('随机梯度下降法')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "\n",
    "# 4. 定义随机梯度下降函数\n",
    "def random_gradient_descent(X, y, theta, num_iters,n_porchs):\n",
    "    for i in range(n_porchs):\n",
    "        for j in range(num_iters):\n",
    "            random_index = np.random.randint(num)    # 随机选取样本\n",
    "            xi = X[ random_index:random_index+1]\n",
    "            yi = y[random_index:random_index+1]\n",
    "            \n",
    "            prediction = np.dot(xi, theta)\n",
    "            theta =theta- learning_rate_schedule(n_porchs*num_iters+j) * ((prediction - yi).dot(xi)).T\n",
    "            if  i<3 and j<10:\n",
    "                plt.plot(x, X.dot(theta) , color='blue')\n",
    "            theta_route_random.append(theta)\n",
    "\n",
    "# 5. 调用随机梯度下降函数,并显示图像\n",
    "random_gradient_descent(X, y, theta, num_iters,n_porch)\n",
    "plt.show()\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T10:51:29.190037200Z",
     "start_time": "2024-04-15T10:51:28.926138100Z"
    }
   },
   "id": "9f057eb0bdf8e96f"
  },
  {
   "cell_type": "markdown",
   "source": [
    "代码求解-梯度下降法-小批量梯度下降法"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "c6de40a8b8081438"
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "经过训练的theta值为 [[6.1908999 ]\n",
      " [3.12021405]]\n"
     ]
    }
   ],
   "source": [
    "# 1. 导入依赖\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 2. 定义参数\n",
    "learning_rate = 0.01\n",
    "num_iters = 500\n",
    "batch_size = 8\n",
    "theta = np.zeros((2,1)) # 定义初始theta为2*1的零向量\n",
    "num = len(x)\n",
    "n_porchs = 50\n",
    "theta_route_mini_batch = []\n",
    "\n",
    "\n",
    "t=0\n",
    "\n",
    "# 3. 训练数据\n",
    "for i in range(n_porchs):\n",
    "    # 3.1 洗牌操作\n",
    "    indices = np.random.permutation(num)\n",
    "    X_batch = X[indices[:batch_size]]\n",
    "    y_batch = y[indices[:batch_size]]\n",
    "    \n",
    "    # 3.2 遍历所有的梯度样本\n",
    "    for j in range(0, num, batch_size):\n",
    "        t+=1\n",
    "        X_batch = X[j:j+batch_size]\n",
    "        y_batch = y[j:j+batch_size]\n",
    "        hypothesis = np.dot(X_batch, theta)\n",
    "        theta = theta - 1/batch_size * learning_rate_schedule(batch_size*num_iters+t) * np.dot(X_batch.T , (hypothesis - y_batch))\n",
    "        theta_route_mini_batch.append(theta)\n",
    "\n",
    "\n",
    "print(\"经过训练的theta值为\",theta)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T11:00:33.292261500Z",
     "start_time": "2024-04-15T11:00:33.253524Z"
    }
   },
   "id": "1ec105d4a605f071"
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x800 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 导入依赖\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 2. 定义各类梯度下降的theta变化\n",
    "theta_route_batch=np.array(theta_route_batch)\n",
    "theta_route_random=np.array(theta_route_random)\n",
    "theta_route_mini_batch=np.array(theta_route_mini_batch)\n",
    "\n",
    "# 3. 绘制theta变化曲线\n",
    "plt.figure(figsize=(10, 8))\n",
    "\n",
    "plt.plot(theta_route_batch[:,0],theta_route_batch[:,1],'r-s',linewidth=1, label='批量梯度下降')\n",
    "plt.plot(theta_route_random[:,0],theta_route_random[:,1],'g-+',linewidth=1, label='随机梯度下降')\n",
    "plt.plot(theta_route_mini_batch[:,0],theta_route_mini_batch[:,1],'b-o',linewidth=1, label='小批量梯度下降')\n",
    "\n",
    "# plt.axis([ 2.0,4.0,3.5, 4.5])\n",
    "plt.xlim(3,8)\n",
    "plt.ylim(2,5)# 1. 导入依赖\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 2. 定义各类梯度下降的theta变化\n",
    "theta_route_batch=np.array(theta_route_batch)\n",
    "theta_route_random=np.array(theta_route_random)\n",
    "theta_route_mini_batch=np.array(theta_route_mini_batch)\n",
    "\n",
    "# 3. 绘制theta变化曲线\n",
    "plt.figure(figsize=(10, 8))\n",
    "\n",
    "plt.plot(theta_route_batch[:,0],theta_route_batch[:,1],'r-s',linewidth=1, label='批量梯度下降')\n",
    "plt.plot(theta_route_random[:,0],theta_route_random[:,1],'g-+',linewidth=1, label='随机梯度下降')\n",
    "plt.plot(theta_route_mini_batch[:,0],theta_route_mini_batch[:,1],'b-o',linewidth=1, label='小批量梯度下降')\n",
    "\n",
    "# plt.axis([ 2.0,4.0,3.5, 4.5])\n",
    "plt.xlim(3,8)\n",
    "plt.ylim(2,5)\n",
    "plt.title('theta变化曲线')\n",
    "plt.xlabel('theta值-2')\n",
    "plt.ylabel('theta值-1')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.title('theta变化曲线')\n",
    "plt.xlabel('theta值-2')\n",
    "plt.ylabel('theta值-1')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T11:01:02.445758600Z",
     "start_time": "2024-04-15T11:01:02.277549200Z"
    }
   },
   "id": "9e2cd9b8fc2814f4"
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[0.02916582],\n        [0.03153196]],\n\n       [[0.04573354],\n        [0.05092408]],\n\n       [[0.07459674],\n        [0.08210762]],\n\n       [[0.09098872],\n        [0.10128359]],\n\n       [[0.11955258],\n        [0.13212252]],\n\n       [[0.13577072],\n        [0.15108469]],\n\n       [[0.1640385 ],\n        [0.18158275]],\n\n       [[0.18008469],\n        [0.20033345]],\n\n       [[0.20805959],\n        [0.23049436]],\n\n       [[0.2239357 ],\n        [0.24903589]],\n\n       [[0.2516209 ],\n        [0.27886333]],\n\n       [[0.26732878],\n        [0.29719797]],\n\n       [[0.29472742],\n        [0.32669556]],\n\n       [[0.3102689 ],\n        [0.34482557]],\n\n       [[0.33738408],\n        [0.37399691]],\n\n       [[0.35276096],\n        [0.39192452]],\n\n       [[0.37959576],\n        [0.42077315]],\n\n       [[0.39480983],\n        [0.43850057]],\n\n       [[0.42136729],\n        [0.46703001]],\n\n       [[0.43642032],\n        [0.48455941]],\n\n       [[0.46270345],\n        [0.51277315]],\n\n       [[0.47759717],\n        [0.53010669]],\n\n       [[0.50360894],\n        [0.55800815]],\n\n       [[0.5183451 ],\n        [0.57514798]],\n\n       [[0.54408845],\n        [0.60274056]],\n\n       [[0.55866875],\n        [0.61968877]],\n\n       [[0.58414659],\n        [0.64697585]],\n\n       [[0.59857273],\n        [0.66373454]],\n\n       [[0.62378794],\n        [0.69071942]],\n\n       [[0.63806158],\n        [0.70729066]],\n\n       [[0.663017  ],\n        [0.73397664]],\n\n       [[0.6771398 ],\n        [0.75036246]],\n\n       [[0.70183825],\n        [0.77675281]],\n\n       [[0.71581185],\n        [0.79295523]],\n\n       [[0.74025611],\n        [0.81905315]],\n\n       [[0.75408213],\n        [0.83507417]],\n\n       [[0.77827495],\n        [0.86088285]],\n\n       [[0.79195498],\n        [0.87672445]],\n\n       [[0.8158991 ],\n        [0.90224704]],\n\n       [[0.82943473],\n        [0.91791117]],\n\n       [[0.85313282],\n        [0.94315078]],\n\n       [[0.86652562],\n        [0.95863938]],\n\n       [[0.88998036],\n        [0.98359908]],\n\n       [[0.90323188],\n        [0.99891406]],\n\n       [[0.9264459 ],\n        [1.02359691]],\n\n       [[0.93955766],\n        [1.03874016]],\n\n       [[0.96253357],\n        [1.06314916]],\n\n       [[0.97550709],\n        [1.07812256]],\n\n       [[0.99824747],\n        [1.1022607 ]],\n\n       [[1.01108425],\n        [1.11706608]],\n\n       [[1.03359165],\n        [1.14093631]],\n\n       [[1.04629317],\n        [1.15557551]],\n\n       [[1.0685701 ],\n        [1.17918073]],\n\n       [[1.08113784],\n        [1.19365557]],\n\n       [[1.1031868 ],\n        [1.21699867]],\n\n       [[1.11562219],\n        [1.23131093]],\n\n       [[1.13744565],\n        [1.25439477]],\n\n       [[1.14975014],\n        [1.26854622]],\n\n       [[1.17135054],\n        [1.29137361]],\n\n       [[1.18352554],\n        [1.305366  ]],\n\n       [[1.20490529],\n        [1.32793974]],\n\n       [[1.21695221],\n        [1.3417748 ]],\n\n       [[1.2381137 ],\n        [1.36409765]],\n\n       [[1.25003392],\n        [1.3777771 ]],\n\n       [[1.27097951],\n        [1.39985177]],\n\n       [[1.2827744 ],\n        [1.4133773 ]],\n\n       [[1.30350643],\n        [1.43520651]],\n\n       [[1.31517736],\n        [1.4485798 ]],\n\n       [[1.33569813],\n        [1.47016621]],\n\n       [[1.34724644],\n        [1.48338892]],\n\n       [[1.36755824],\n        [1.50473517]],\n\n       [[1.37898525],\n        [1.51780893]],\n\n       [[1.39909035],\n        [1.53891764]],\n\n       [[1.41039738],\n        [1.55184408]],\n\n       [[1.430298  ],\n        [1.57271782]],\n\n       [[1.44148634],\n        [1.58549854]],\n\n       [[1.4611847 ],\n        [1.60613988]],\n\n       [[1.47225564],\n        [1.61877646]],\n\n       [[1.49175392],\n        [1.63918792]],\n\n       [[1.50270875],\n        [1.65168194]],\n\n       [[1.52200911],\n        [1.67186602]],\n\n       [[1.53284906],\n        [1.68421903]],\n\n       [[1.55195365],\n        [1.7041782 ]],\n\n       [[1.56267998],\n        [1.71639173]],\n\n       [[1.5815909 ],\n        [1.73612844]],\n\n       [[1.59220484],\n        [1.74820401]],\n\n       [[1.6109242 ],\n        [1.76772068]],\n\n       [[1.62142695],\n        [1.77965979]],\n\n       [[1.63995681],\n        [1.7989588 ]],\n\n       [[1.65034959],\n        [1.81076295]],\n\n       [[1.668692  ],\n        [1.82984668]],\n\n       [[1.678976  ],\n        [1.84151732]],\n\n       [[1.69713298],\n        [1.8603881 ]],\n\n       [[1.70730937],\n        [1.87192669]],\n\n       [[1.72528293],\n        [1.89058685]],\n\n       [[1.73535288],\n        [1.90199483]],\n\n       [[1.753145  ],\n        [1.92044664]],\n\n       [[1.76310965],\n        [1.93172543]],\n\n       [[1.78072229],\n        [1.94997116]],\n\n       [[1.79058279],\n        [1.96112217]]])"
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_route_mini_batch"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T11:00:03.806139800Z",
     "start_time": "2024-04-15T11:00:03.776841600Z"
    }
   },
   "id": "5e9b317f3c94626e"
  },
  {
   "cell_type": "markdown",
   "source": [
    "多项式回归"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "ea0a6e4f47a94207"
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7.46800681]\n",
      "[[2.91538646 1.99508195]]\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 多项式回归\n",
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 2. 生成数据\n",
    "np.random.seed(42)\n",
    "sample_size = 100\n",
    "x = 6*np.random.rand(sample_size, 1)-3\n",
    "y = 3*x+2*x**2+np.random.rand(sample_size,1)*15\n",
    "\n",
    "# 3. 画图,观察数据分布\n",
    "plt.scatter(x, y, color='blue',s=10)\n",
    "plt.title('多项式回归数据')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()\n",
    "\n",
    "# 4. 对数据x进行特征变换\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "x_poly = poly_features.fit_transform(x)  # 特征变换,在转换的同时记录转换规则，便于下面使用\n",
    "from sklearn.linear_model import LinearRegression\n",
    "linear_regressor = LinearRegression()\n",
    "linear_regressor.fit(x_poly, y)\n",
    "print(linear_regressor.intercept_)  # 截距\n",
    "print(linear_regressor.coef_)   # 系数\n",
    "\n",
    "# 5. 画拟合曲线\n",
    "x_plot = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "x_poly_plot = poly_features.transform(x_plot)\n",
    "y_plot = linear_regressor.predict(x_poly_plot)\n",
    "plt.scatter(x, y, color='red')   # 原始数据     \n",
    "plt.plot(x_plot, y_plot, color='blue')   # 拟合曲线\n",
    "plt.title('多项式回归拟合曲线')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T12:32:12.840865Z",
     "start_time": "2024-04-15T12:32:12.673582200Z"
    }
   },
   "id": "b43003cc80ed8532"
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.65354699]\n",
      " [32.28533748]\n",
      " [12.76635628]\n",
      " [10.10522483]\n",
      " [15.94110129]\n",
      " [ 6.06774825]\n",
      " [12.26213562]\n",
      " [27.57855552]\n",
      " [ 5.98818838]\n",
      " [ 8.01718728]\n",
      " [12.26521704]\n",
      " [26.77539603]\n",
      " [27.8867362 ]\n",
      " [12.90182237]\n",
      " [11.06285106]\n",
      " [14.58994475]\n",
      " [11.29056069]\n",
      " [ 3.28829408]\n",
      " [12.49686191]\n",
      " [ 7.47039773]\n",
      " [15.02575148]\n",
      " [16.3097157 ]\n",
      " [ 4.13933279]\n",
      " [ 0.53115135]\n",
      " [ 2.76723609]\n",
      " [17.39520782]\n",
      " [13.35844984]\n",
      " [13.18176723]\n",
      " [ 2.38265678]\n",
      " [14.30823739]\n",
      " [ 9.02971683]\n",
      " [ 5.2169648 ]\n",
      " [ 7.58987759]\n",
      " [27.65203948]\n",
      " [38.13557185]\n",
      " [17.2470388 ]\n",
      " [ 7.01356327]\n",
      " [14.95785884]\n",
      " [11.21444869]\n",
      " [13.75736026]\n",
      " [17.91896456]\n",
      " [ 3.6915937 ]\n",
      " [14.68689252]\n",
      " [23.94405168]\n",
      " [ 4.12011809]\n",
      " [ 5.38047682]\n",
      " [ 8.30686014]\n",
      " [ 7.93040596]\n",
      " [ 1.77005951]\n",
      " [ 5.65788059]\n",
      " [37.95321162]\n",
      " [13.99608026]\n",
      " [23.99187504]\n",
      " [25.67266555]\n",
      " [17.23703365]\n",
      " [24.03897196]\n",
      " [14.86726455]\n",
      " [12.60668799]\n",
      " [10.26956611]\n",
      " [ 9.9758747 ]\n",
      " [ 4.40521591]\n",
      " [ 9.13312113]\n",
      " [23.20114202]\n",
      " [ 6.93559202]\n",
      " [ 0.86642534]\n",
      " [13.42931973]\n",
      " [ 7.6316867 ]\n",
      " [14.8125804 ]\n",
      " [ 5.98605385]\n",
      " [34.69559902]\n",
      " [20.40031071]\n",
      " [ 1.36130102]\n",
      " [16.3853971 ]\n",
      " [16.24088806]\n",
      " [16.48190122]\n",
      " [10.51361384]\n",
      " [20.54523958]\n",
      " [11.19736695]\n",
      " [12.94563334]\n",
      " [ 5.77253095]\n",
      " [21.14463198]\n",
      " [ 5.01604392]\n",
      " [12.88544314]\n",
      " [19.01879519]\n",
      " [ 3.03919936]\n",
      " [ 8.95344319]\n",
      " [20.18701201]\n",
      " [12.16643483]\n",
      " [25.70981502]\n",
      " [ 3.18323776]\n",
      " [ 4.96825266]\n",
      " [20.57072297]\n",
      " [23.09703833]\n",
      " [10.86986385]\n",
      " [15.24932741]\n",
      " [ 5.12923597]\n",
      " [11.33573438]\n",
      " [12.53041412]\n",
      " [20.98018502]\n",
      " [15.71011645]]\n"
     ]
    }
   ],
   "source": [
    "print(y)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T12:33:44.419865Z",
     "start_time": "2024-04-15T12:33:44.362540600Z"
    }
   },
   "id": "3b4feeefdd24d73d"
  },
  {
   "cell_type": "markdown",
   "source": [
    "多项式回归对比-管道实现"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "866e51138cdf79b4"
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x800 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# 2. 循环进行多项式回归\n",
    "plt.figure(figsize=(10, 8))\n",
    "for style,width,degree in [('g-',1,1),('b--',1,2),('r-.',1,100)]:\n",
    "    # 2.1 特征变换\n",
    "    polynomial_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    # 2.2 定义标准\n",
    "    std = StandardScaler()\n",
    "    # 2.3 线性回归\n",
    "    linear_regression = LinearRegression()\n",
    "    # 2.4 管道\n",
    "    model = Pipeline([(\"polynomial_features\", polynomial_features),\n",
    "                      (\"std\",std),\n",
    "                      (\"linear_regression\", linear_regression)])\n",
    "\n",
    "    # 2.5 训练模型\n",
    "    model.fit(x, y)\n",
    "    # 2.6 画拟合曲线\n",
    "    x_plot = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "    y_plot_test = model.predict(x_plot)\n",
    "    plt.plot(x_plot, y_plot_test, style, linewidth=width,\n",
    "             label=\"degree %d\" % degree)\n",
    "\n",
    "# 3. 画原始数据\n",
    "plt.scatter(x, y, color='blue')\n",
    "plt.title('多项式回归拟合曲线')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.axis([-3,3,-2,30])\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T13:01:22.248495800Z",
     "start_time": "2024-04-15T13:01:20.969957600Z"
    }
   },
   "id": "1fd24ac9ab829bda"
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "206a7dbbc0066f90"
  },
  {
   "cell_type": "markdown",
   "source": [
    "样本数目对拟合曲线的影响"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "541eac72b0f37846"
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x800 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 样本数目vs拟合\n",
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import mean_squared_error  # 引入模型标准--均方误差\n",
    "from sklearn.model_selection import train_test_split  # 引入数据集划分\n",
    "from sklearn.linear_model import LinearRegression  # 引入线性回归模型\n",
    "plt.figure(figsize=(10, 8))\n",
    "\n",
    "# 2. 定义模型处理函数\n",
    "def sample_model_fit(model,x, y):\n",
    "    # 2.1 划分数据集\n",
    "    x_train, x_valid, y_train, y_valid = train_test_split(x, y, test_size=0.2, random_state=0)\n",
    "    train_errors,valid_errors = [],[]\n",
    "    # 2.2 循环遍历不同样本数目\n",
    "    for i in range(1,100,1):\n",
    "        # 2.2.1 选取不同样本数目\n",
    "        x_train_sample = x_train[:i]\n",
    "        y_train_sample = y_train[:i]\n",
    "        # 2.2.2 训练模型\n",
    "        model.fit(x_train_sample, y_train_sample)\n",
    "        # 2.2.3 计算训练集和验证集的均方误差\n",
    "        y_train_predict = model.predict(x_train_sample)\n",
    "        y_valid_predict = model.predict(x_valid)\n",
    "        train_errors.append(np.sqrt(mean_squared_error(y_train_sample, y_train_predict)))\n",
    "        valid_errors.append(np.sqrt(mean_squared_error(y_valid, y_valid_predict)))\n",
    "    # 2.3 画图\n",
    "    plt.plot(range(1,100,1), train_errors, 'b-', label='训练集')\n",
    "    plt.plot(range(1,100,1), valid_errors, 'r-', label='验证集')\n",
    "    plt.xlabel('sample num')\n",
    "    plt.ylabel('均方误差')\n",
    "   \n",
    "\n",
    "# 3. 画不同样本数目对拟合曲线的影响\n",
    "model = LinearRegression()\n",
    "sample_model_fit(model,x, y)\n",
    "plt.title('样本数目对拟合曲线的影响')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T13:34:50.899902700Z",
     "start_time": "2024-04-15T13:34:50.723525Z"
    }
   },
   "id": "31f556491237c5ee"
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# 2. 定义管道，即模型\n",
    "model = Pipeline([(\"polynomial_features\", PolynomialFeatures(degree=100, include_bias=False)),\n",
    "                  (\"linear_regression\", LinearRegression())])\n",
    "\n",
    "# 3. 对比不同特征值对拟合曲线的影响\n",
    "sample_model_fit(model,x, y)\n",
    "plt.title('不同特征值对拟合曲线的影响')\n",
    "plt.legend()\n",
    "plt.ylim(0,50)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-15T13:52:54.481737400Z",
     "start_time": "2024-04-15T13:52:51.265869200Z"
    }
   },
   "id": "6e61c8de658b356e"
  },
  {
   "cell_type": "markdown",
   "source": [
    "岭回归--解决过拟合问题"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "9af831b75b2719bc"
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 岭回归\n",
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号\n",
    "plt.rcParams['font.size']\n",
    "\n",
    "# 2. 重新训练测试数据\n",
    "np.random.seed(42)\n",
    "sample_size = 100\n",
    "x_ridge = 6*np.random.rand(sample_size, 1)-3\n",
    "y_ridge = 3*x_ridge+2*x_ridge**2+np.random.rand(sample_size,1)*15\n",
    "x_new = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "\n",
    "# 3. 定义不同模型，不同alpha值对拟合曲线的方法(ploynominal:是否特征变换)\n",
    "def model_fit(model_class,alpha_list,ploynominal=False,**augs):\n",
    "    for alpha,style in zip(alpha_list,['g-','b--','r-.' ]):\n",
    "        model = model_class(alpha=alpha,**augs)\n",
    "        if ploynominal:\n",
    "            model = Pipeline([(\"polynomial_features\", PolynomialFeatures(degree=5, include_bias=False)),\n",
    "                               (\"lin_reg\",model)])\n",
    "        model.fit(x_ridge, y_ridge)\n",
    "        model.predict(x_new)\n",
    "        plt.plot(x_new, model.predict(x_new), label=\"alpha=%.2f\" % alpha)\n",
    "    plt.title('不同回归的回归拟合曲线')\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.legend()\n",
    "    \n",
    "\n",
    "# 4. 画不同alpha值对拟合曲线的影响\n",
    "plt.scatter(x_ridge, y_ridge, color='blue')\n",
    "alpha_list = [1, 100, 10000]\n",
    "model_fit(Ridge,alpha_list,ploynominal=True)\n",
    "plt.show()     "
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-16T06:00:51.187635Z",
     "start_time": "2024-04-16T06:00:51.036211100Z"
    }
   },
   "id": "5435a6ea153a8cce"
  },
  {
   "cell_type": "markdown",
   "source": [
    "lasso回归--解决过拟合问题"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "336c43ea9c2661e"
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lasso回归\n",
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号\n",
    "plt.rcParams['font.size']\n",
    "\n",
    "# 2. 重新训练测试数据\n",
    "np.random.seed(42)\n",
    "sample_size = 100\n",
    "x_lasso = 6*np.random.rand(sample_size, 1)-3\n",
    "y_lasso = 3*x_lasso+2*x_lasso**2+np.random.rand(sample_size,1)*15\n",
    "x_new = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "\n",
    "#  画不同alpha值对拟合曲线的影响\n",
    "plt.scatter(x_lasso, y_lasso, color='blue')# lasso回归\n",
    "# 1. 导入依赖 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号\n",
    "plt.rcParams['font.size']\n",
    "\n",
    "# 2. 重新训练测试数据\n",
    "np.random.seed(42)\n",
    "sample_size = 100\n",
    "x_lasso = 6*np.random.rand(sample_size, 1)-3\n",
    "y_lasso = 3*x_lasso+2*x_lasso**2+np.random.rand(sample_size,1)*15\n",
    "x_new = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "\n",
    "#  画不同alpha值对拟合曲线的影响\n",
    "plt.scatter(x_lasso, y_lasso, color='blue')\n",
    "alpha_list = [1, 10, 100]\n",
    "model_fit(Lasso,alpha_list,ploynominal=True)\n",
    "plt.show()\n",
    "alpha_list = [1, 10, 100]\n",
    "model_fit(Lasso,alpha_list,ploynominal=True)\n",
    "plt.show()     "
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-16T06:04:59.835480700Z",
     "start_time": "2024-04-16T06:04:59.691718800Z"
    }
   },
   "id": "84708555e8231cdc"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
